Mop heads incorporating tubular strand elements of so-called “edgeless” construction are known. One such construction, which is marketed by Contec Inc. of Spartanburg, S.C., is formed from a skein of circular knit material of tubular construction which is formed on a winding apparatus using a pair of support bars which rotate relative to one another. The skein structure is formed from a single continuous tube of the knit material. Upon removal from the winding apparatus, the skein thus has an interior and two ends formed by the reverse folds in the knit tube where it has been passed around the winder bars. The skein structure is thereafter inserted into a relatively narrow width containment sleeve which is seamed to the interior of the skein structure at a substantially central location to contain the tubular elements in the wound structure. Seams are also applied at slightly inboard positions relative to the folded over ends of the skein structure so as to avoid undue spreading of the individual folded over elements. The mop head so formed is thereafter attached to a handle at the central containment sleeve. Importantly, the prior mop heads formed in this manner have utilized a circular